Question

A very long cylindrical wire of radius R carries a current $I_0$ uniformly distributed across the cross-section of the wire, calculate the magnetic flux through a rectangle that has one side of length w s running down the centre of the wire and another side of length R, shown in figure

• A. $\frac{{\mu }_0{I}_0\times wR}{4\pi }$
• B. $\frac{{\mu }_0{I}_{0}w}{4\pi }$
• C. $\frac{{\mu }_0{I}_{0}R}{4\pi w}$
• D. None of these

Answer 1

The correct option is C $\frac{{\mu }_0{I}_{0}R}{4\pi w}$

Radius $=R$. (one side)

Current $=I_0$

$\phi =$ magnetic flux

length $=W$

another side $=L$

$\frac{{\mu }_0{I}_0{R}^2}{4\pi W}$ $\phi =r_{0}nI$

$=\frac{{\mu }_0}{4\pi }\times$ $=\frac{{\mu }_0}{4\pi }\times I_0\times \frac{R^2}{WR}$

$=\frac{{\mu }_0}{4\pi }\times I_0\times \frac{R}{W}$